RMP Lecture Notes

Ideal Gases

When you start a calculation involving a fluid, one of the first questions should be: "Is it incompressible?"

An incompressible fluid is one whose density and related properties are relatively insensitive to pressure. Most familiar liquids are incompressible.

Gases and vapors are generally not incompressible; therefore, their properties are typically functions of both T and P. In order to relate properties at one condition (T₁,P₁,V₁) to properties at another (T₂,P₂,V₂) we use the PVT relationship provided by an equation of state.

The simplest equation of state is the ideal gas equation. It is not valid at high pressures or low temperatures. Later we'll cover real gases -- those that do not behave ideally.

Ideal Gas Equation

The ideal gas equation assumes perfect collisions between all molecules and container walls, negligible molecular interaction, and negligible volume occupied by the molecules themselves.

This equation requires absolute P and T values be used. It is the same for any amount and any composition of gas, as long as the ideal gas assumptions are valid.

EXAMPLE: Ideal Gases

Himmelblau, 1974, p. 150 A cylinder contains 1.000 cubic feet of oxygen at 70 F and 200 psig. What will be the volume of this gas in a balloon at 90 F and 4.00 in H₂O above atmospheric? The barometer reads 29.92 in Hg.

Since no gas is added or removed, the number of moles is constant Example

We want to find the volume in the balloon, so Example

Putting the pressures into consistent units yields Example

The temperatures are: Example

Often, particularly in thermodynamics, you will see the ideal gas equation in terms of the molar volume:

Data is often given at standard conditions

which leads to the abbreviations STP for "standard temperature and pressure" and SCF for "standard cubic feet" (also be prepared for "standard cubic feet per hour", SCFH, "standard cubic feet per minute", SCFM, etc.). Some petroleum industry references use 60 F instead of 32 F.

Flowsheets, design bases, problem statements, etc., often state flows in SCF even if the actual (real) conditions are not standard. This is done so that rates are readily compared -- using SCF or SCM is nearly the same as using molar rates.

You must convert to actual conditions whenever you need volume or volumetric flow, or whenever you need to determine velocity.

Mixtures of Ideal Gases

Suppose you have a mixture of gases, each is ideal, and the mixture is ideal. A mixture of ideal gases is itself an ideal gas, wo you can write

The composition of the mixture can be expressed using mole fractions Ideal Gas Mixtures

and since each component is ideal Ideal Gas Mixtures

but

, so something else has to be different if this is to make sense.

Normally, we address the problem by defining the partial pressure

Dividing by the total pressure of the system shows that Partial Pressure

and consequently Partial Pressure

which you may recognize as Dalton's Law. A warning -- partial pressures aren't defined for anything other than ideal gas mixtures, so we'll have do develop alternatives in Thermo II.

Occasionally, it is more convenient to use the pure component volume given by

(In Thermo II, we'll call this the partial molar volume.)

As a consequence of this behavior we can note that for an ideal gas mixture (but ONLY for ideal gases), volume fractions are the same as mole fractions.

References:

Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2nd Edition, John Wiley, 1986, pp. 185-93.
Felder, R.M. and R.W. Rousseau, Elementary Principles of Chemical Processes, 2005 3rd Edition, 2005, p. 191-99.

R.M. Price
Original: 6/20/94
Modified: 10/11/96; 1/12/2005